Population balance in confined comminution using a physically based probabilistic approach for polydisperse granular materials

Abstract

A novel, simplified approach is presented in order to compute variations of grading in granular assemblies during confined comminution under quasi-static compression. The method is based on a population balance equation and requires a breakage probability, considered here as a probabilistic phenomenon that takes into account the particle strength and the loading condition of individual grains. Under basic assumptions, a simple breakage probability can be defined in order to get a valuable result for engineering applications and powder technology. The size effect in the strength of individual particles is introduced according to Weibull’s theory. The particle loading and the cushioning effect in the granular packing are accounted for by considering the orientations of the contact forces obtained from 3D discrete element method simulations of highly polydisperse materials. The method proposed could have a value for engineering purposes in powder technology and geomechanics and gives a general framework for further research developments based on population balance.